Principle of Explosion

The principle of explosion, (Latin: ex falso quodlibet or ex contradictione sequitur quodlibet, "from a contradiction, anything follows") or the principle of Pseudo-Scotus, is the law of classical logic, intuitionistic logic and similar logical systems, according to which any statement can be proven from a contradiction. That is, once a contradiction has been asserted, any proposition (or its negation) can be inferred from it. In symbolic terms, the principle of explosion can be expressed in the following way (where "" symbolizes the relation of logical consequence):

or

.

This can be read as, "If one claims something is both true and not true, one can logically derive any conclusion ."